We report results of ac impedance measurements which we have obtained from intrinsic indium oxide films under UV irradiation and in darkness. We find two distinct contributions to the ac conductivity. One of them is brought about by grain boundaries, and the other one by inversion layers, which are on grain surfaces. In addition, we have found that photocurrents relax extremely slowly in these films. All of this fits consistently within a model in which mobile holes in inversion layers are responsible for recently reported $p$-type dc conductivity.